Advice about taking mathematical analysis classCan anybody recommend a website or other type of resource which contains real Analysis-type questions and their solutions?Rudin against Pugh for Textbook for First Course in Real AnalysisSelf-study Real analysis Tao or Rudin?How to learn inequalities and become good at proving them?How can I pick up analysis quickly?Can I Start Analysis? Seeking Your Advice on My Journey to Mathematics!Selecting the Real Analysis TextbooksTips for understanding and effectively studying mathematical analysisHow important is the choice of books in studying Analysis?Supplementary Books to Complex Analysis of Rudin's RCA?Order of study in mathematical analysis textbooks.

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Advice about taking mathematical analysis class


Can anybody recommend a website or other type of resource which contains real Analysis-type questions and their solutions?Rudin against Pugh for Textbook for First Course in Real AnalysisSelf-study Real analysis Tao or Rudin?How to learn inequalities and become good at proving them?How can I pick up analysis quickly?Can I Start Analysis? Seeking Your Advice on My Journey to Mathematics!Selecting the Real Analysis TextbooksTips for understanding and effectively studying mathematical analysisHow important is the choice of books in studying Analysis?Supplementary Books to Complex Analysis of Rudin's RCA?Order of study in mathematical analysis textbooks.













5












$begingroup$


I apologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really excited about it because it seems so interesting and fun. However, I know this will be quite a challenging course and I am not going to give up. So I'm wondering if anyone could give me some advice on how to conquer this class besides the obvious going to class and doing the homework?



We have to use Rudin's Mathematical Analysis as a textbook, and from what I have heard it seems to be the "bible" of mathematical analysis. So I would think reading the book will be a good way to keep up. But any other suggestions or tips from the pros? Any supplementary books that could explain certain topics in a more "dumbed down" way than Rudin does?










share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
    $endgroup$
    – Rankeya
    Dec 4 '12 at 16:19











  • $begingroup$
    @Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
    $endgroup$
    – TheHopefulActuary
    Dec 4 '12 at 16:22






  • 3




    $begingroup$
    One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
    $endgroup$
    – Thomas Andrews
    Dec 4 '12 at 16:27















5












$begingroup$


I apologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really excited about it because it seems so interesting and fun. However, I know this will be quite a challenging course and I am not going to give up. So I'm wondering if anyone could give me some advice on how to conquer this class besides the obvious going to class and doing the homework?



We have to use Rudin's Mathematical Analysis as a textbook, and from what I have heard it seems to be the "bible" of mathematical analysis. So I would think reading the book will be a good way to keep up. But any other suggestions or tips from the pros? Any supplementary books that could explain certain topics in a more "dumbed down" way than Rudin does?










share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
    $endgroup$
    – Rankeya
    Dec 4 '12 at 16:19











  • $begingroup$
    @Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
    $endgroup$
    – TheHopefulActuary
    Dec 4 '12 at 16:22






  • 3




    $begingroup$
    One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
    $endgroup$
    – Thomas Andrews
    Dec 4 '12 at 16:27













5












5








5


1



$begingroup$


I apologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really excited about it because it seems so interesting and fun. However, I know this will be quite a challenging course and I am not going to give up. So I'm wondering if anyone could give me some advice on how to conquer this class besides the obvious going to class and doing the homework?



We have to use Rudin's Mathematical Analysis as a textbook, and from what I have heard it seems to be the "bible" of mathematical analysis. So I would think reading the book will be a good way to keep up. But any other suggestions or tips from the pros? Any supplementary books that could explain certain topics in a more "dumbed down" way than Rudin does?










share|cite|improve this question











$endgroup$




I apologize if this isn't the place to ask, if it's not could you let me know and I will take it to meta? Anyway, so I am planning on taking a mathematical analysis course next spring, and I'm really excited about it because it seems so interesting and fun. However, I know this will be quite a challenging course and I am not going to give up. So I'm wondering if anyone could give me some advice on how to conquer this class besides the obvious going to class and doing the homework?



We have to use Rudin's Mathematical Analysis as a textbook, and from what I have heard it seems to be the "bible" of mathematical analysis. So I would think reading the book will be a good way to keep up. But any other suggestions or tips from the pros? Any supplementary books that could explain certain topics in a more "dumbed down" way than Rudin does?







real-analysis reference-request soft-question advice






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 21 at 12:47


























community wiki





4 revs, 3 users 75%
TheHopefulActuary








  • 1




    $begingroup$
    Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
    $endgroup$
    – Rankeya
    Dec 4 '12 at 16:19











  • $begingroup$
    @Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
    $endgroup$
    – TheHopefulActuary
    Dec 4 '12 at 16:22






  • 3




    $begingroup$
    One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
    $endgroup$
    – Thomas Andrews
    Dec 4 '12 at 16:27












  • 1




    $begingroup$
    Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
    $endgroup$
    – Rankeya
    Dec 4 '12 at 16:19











  • $begingroup$
    @Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
    $endgroup$
    – TheHopefulActuary
    Dec 4 '12 at 16:22






  • 3




    $begingroup$
    One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
    $endgroup$
    – Thomas Andrews
    Dec 4 '12 at 16:27







1




1




$begingroup$
Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
$endgroup$
– Rankeya
Dec 4 '12 at 16:19





$begingroup$
Dear @Kyle: You should first attend the class and judge for yourself whether the professor is an effective instructor or not. That being said, start reading on your own, and do the problems in Rudin.
$endgroup$
– Rankeya
Dec 4 '12 at 16:19













$begingroup$
@Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
$endgroup$
– TheHopefulActuary
Dec 4 '12 at 16:22




$begingroup$
@Rankeya Yes perhaps you're right. I often forget about that. I also thought of another error in my judgement, so I'll change the question a little bit. Thanks for the reminder.
$endgroup$
– TheHopefulActuary
Dec 4 '12 at 16:22




3




3




$begingroup$
One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
$endgroup$
– Thomas Andrews
Dec 4 '12 at 16:27




$begingroup$
One part of this sort of mathematics that might be new to you is the definitions. I found it useful to copy the definitions to a separate page as I was going along, so when, several pages later, Rudin uses a term, I didn't need to flip back through the book to find the definition.
$endgroup$
– Thomas Andrews
Dec 4 '12 at 16:27










3 Answers
3






active

oldest

votes


















18












$begingroup$

I wouldn't take ratings/reviews from ratemyprofessor.com too literally. After all, it seems to me that it is much more likely that disgruntled students are going to go out of their way to (be)rate a professor than are those who have no complaints and would otherwise rate highly.



You've got the opportunity to get a "head start": use that opportunity to "preview" the text. E.g., read the Intro, the Table of Contents, and start tackling the first chapter prior to the start of class, if possible. Once class begins:



  • Yes, go to class!


  • Yes, do the homework!


  • Yes, read the book!:


and



  • "Write the book!"
    (I.e., Take notes; work through all the proofs in the text and fill in any steps that help connect the steps given by Rudin; create a list of definitions and add definitions to that list as you encounter them; work the problems, not just those that are assigned.)


It never hurts to have a supplementary text to refer to, for alternate proofs and explication:



  • E.g., See Serge Lang's Undergraduate Analysis. There is a text available to supplement Lang's text, entitled Problems and Solutions for Undergraduate Analysis.

  • Also see this recent post for some readily available resources to supplement (but not replace!) Rudin's Principles of Mathematical Analysis.


  • And of course, there's math.stackexchange.com, when you're completely stuck!






share|cite|improve this answer











$endgroup$








  • 5




    $begingroup$
    +1 for "write the book" advice, a seldom noted nugget of wisdom :)
    $endgroup$
    – Alex Nelson
    Dec 4 '12 at 16:29










  • $begingroup$
    Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
    $endgroup$
    – TheHopefulActuary
    Dec 4 '12 at 16:47


















1












$begingroup$

The simple "secret" to ace any class is to be ahead of the class. If you can lay your hands on the course material upfront then you can stay ahead. But at the end of the day, you will learn a lot more engaging on sites like stackexchange :)






share|cite|improve this answer











$endgroup$




















    1












    $begingroup$

    This is an old question, but for the benefit of future readers I would like to mention Stephen Abbott's Understanding Analysis. In my opinion, this book is written at a slower pace than Rudin, and takes the reader through each step of the way. It's harder to get lost on this book, for a beginner, compared to Rudin. It goes reasonably deep for a first course as well, ending off with things like Baire's Category Theorem. So while it might not replace Rudin, it is definitely beneficial to use it as a supplement, or to get a "softer" approach first.






    share|cite|improve this answer











    $endgroup$













      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      18












      $begingroup$

      I wouldn't take ratings/reviews from ratemyprofessor.com too literally. After all, it seems to me that it is much more likely that disgruntled students are going to go out of their way to (be)rate a professor than are those who have no complaints and would otherwise rate highly.



      You've got the opportunity to get a "head start": use that opportunity to "preview" the text. E.g., read the Intro, the Table of Contents, and start tackling the first chapter prior to the start of class, if possible. Once class begins:



      • Yes, go to class!


      • Yes, do the homework!


      • Yes, read the book!:


      and



      • "Write the book!"
        (I.e., Take notes; work through all the proofs in the text and fill in any steps that help connect the steps given by Rudin; create a list of definitions and add definitions to that list as you encounter them; work the problems, not just those that are assigned.)


      It never hurts to have a supplementary text to refer to, for alternate proofs and explication:



      • E.g., See Serge Lang's Undergraduate Analysis. There is a text available to supplement Lang's text, entitled Problems and Solutions for Undergraduate Analysis.

      • Also see this recent post for some readily available resources to supplement (but not replace!) Rudin's Principles of Mathematical Analysis.


      • And of course, there's math.stackexchange.com, when you're completely stuck!






      share|cite|improve this answer











      $endgroup$








      • 5




        $begingroup$
        +1 for "write the book" advice, a seldom noted nugget of wisdom :)
        $endgroup$
        – Alex Nelson
        Dec 4 '12 at 16:29










      • $begingroup$
        Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
        $endgroup$
        – TheHopefulActuary
        Dec 4 '12 at 16:47















      18












      $begingroup$

      I wouldn't take ratings/reviews from ratemyprofessor.com too literally. After all, it seems to me that it is much more likely that disgruntled students are going to go out of their way to (be)rate a professor than are those who have no complaints and would otherwise rate highly.



      You've got the opportunity to get a "head start": use that opportunity to "preview" the text. E.g., read the Intro, the Table of Contents, and start tackling the first chapter prior to the start of class, if possible. Once class begins:



      • Yes, go to class!


      • Yes, do the homework!


      • Yes, read the book!:


      and



      • "Write the book!"
        (I.e., Take notes; work through all the proofs in the text and fill in any steps that help connect the steps given by Rudin; create a list of definitions and add definitions to that list as you encounter them; work the problems, not just those that are assigned.)


      It never hurts to have a supplementary text to refer to, for alternate proofs and explication:



      • E.g., See Serge Lang's Undergraduate Analysis. There is a text available to supplement Lang's text, entitled Problems and Solutions for Undergraduate Analysis.

      • Also see this recent post for some readily available resources to supplement (but not replace!) Rudin's Principles of Mathematical Analysis.


      • And of course, there's math.stackexchange.com, when you're completely stuck!






      share|cite|improve this answer











      $endgroup$








      • 5




        $begingroup$
        +1 for "write the book" advice, a seldom noted nugget of wisdom :)
        $endgroup$
        – Alex Nelson
        Dec 4 '12 at 16:29










      • $begingroup$
        Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
        $endgroup$
        – TheHopefulActuary
        Dec 4 '12 at 16:47













      18












      18








      18





      $begingroup$

      I wouldn't take ratings/reviews from ratemyprofessor.com too literally. After all, it seems to me that it is much more likely that disgruntled students are going to go out of their way to (be)rate a professor than are those who have no complaints and would otherwise rate highly.



      You've got the opportunity to get a "head start": use that opportunity to "preview" the text. E.g., read the Intro, the Table of Contents, and start tackling the first chapter prior to the start of class, if possible. Once class begins:



      • Yes, go to class!


      • Yes, do the homework!


      • Yes, read the book!:


      and



      • "Write the book!"
        (I.e., Take notes; work through all the proofs in the text and fill in any steps that help connect the steps given by Rudin; create a list of definitions and add definitions to that list as you encounter them; work the problems, not just those that are assigned.)


      It never hurts to have a supplementary text to refer to, for alternate proofs and explication:



      • E.g., See Serge Lang's Undergraduate Analysis. There is a text available to supplement Lang's text, entitled Problems and Solutions for Undergraduate Analysis.

      • Also see this recent post for some readily available resources to supplement (but not replace!) Rudin's Principles of Mathematical Analysis.


      • And of course, there's math.stackexchange.com, when you're completely stuck!






      share|cite|improve this answer











      $endgroup$



      I wouldn't take ratings/reviews from ratemyprofessor.com too literally. After all, it seems to me that it is much more likely that disgruntled students are going to go out of their way to (be)rate a professor than are those who have no complaints and would otherwise rate highly.



      You've got the opportunity to get a "head start": use that opportunity to "preview" the text. E.g., read the Intro, the Table of Contents, and start tackling the first chapter prior to the start of class, if possible. Once class begins:



      • Yes, go to class!


      • Yes, do the homework!


      • Yes, read the book!:


      and



      • "Write the book!"
        (I.e., Take notes; work through all the proofs in the text and fill in any steps that help connect the steps given by Rudin; create a list of definitions and add definitions to that list as you encounter them; work the problems, not just those that are assigned.)


      It never hurts to have a supplementary text to refer to, for alternate proofs and explication:



      • E.g., See Serge Lang's Undergraduate Analysis. There is a text available to supplement Lang's text, entitled Problems and Solutions for Undergraduate Analysis.

      • Also see this recent post for some readily available resources to supplement (but not replace!) Rudin's Principles of Mathematical Analysis.


      • And of course, there's math.stackexchange.com, when you're completely stuck!







      share|cite|improve this answer














      share|cite|improve this answer



      share|cite|improve this answer








      edited Apr 13 '17 at 12:20


























      community wiki





      8 revs
      amWhy








      • 5




        $begingroup$
        +1 for "write the book" advice, a seldom noted nugget of wisdom :)
        $endgroup$
        – Alex Nelson
        Dec 4 '12 at 16:29










      • $begingroup$
        Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
        $endgroup$
        – TheHopefulActuary
        Dec 4 '12 at 16:47












      • 5




        $begingroup$
        +1 for "write the book" advice, a seldom noted nugget of wisdom :)
        $endgroup$
        – Alex Nelson
        Dec 4 '12 at 16:29










      • $begingroup$
        Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
        $endgroup$
        – TheHopefulActuary
        Dec 4 '12 at 16:47







      5




      5




      $begingroup$
      +1 for "write the book" advice, a seldom noted nugget of wisdom :)
      $endgroup$
      – Alex Nelson
      Dec 4 '12 at 16:29




      $begingroup$
      +1 for "write the book" advice, a seldom noted nugget of wisdom :)
      $endgroup$
      – Alex Nelson
      Dec 4 '12 at 16:29












      $begingroup$
      Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
      $endgroup$
      – TheHopefulActuary
      Dec 4 '12 at 16:47




      $begingroup$
      Yes I must agree with Alex I havent heard that piece of advice before. Are there any other good supplementary books? I just want to check and see if any of them are on reserve at the library.
      $endgroup$
      – TheHopefulActuary
      Dec 4 '12 at 16:47











      1












      $begingroup$

      The simple "secret" to ace any class is to be ahead of the class. If you can lay your hands on the course material upfront then you can stay ahead. But at the end of the day, you will learn a lot more engaging on sites like stackexchange :)






      share|cite|improve this answer











      $endgroup$

















        1












        $begingroup$

        The simple "secret" to ace any class is to be ahead of the class. If you can lay your hands on the course material upfront then you can stay ahead. But at the end of the day, you will learn a lot more engaging on sites like stackexchange :)






        share|cite|improve this answer











        $endgroup$















          1












          1








          1





          $begingroup$

          The simple "secret" to ace any class is to be ahead of the class. If you can lay your hands on the course material upfront then you can stay ahead. But at the end of the day, you will learn a lot more engaging on sites like stackexchange :)






          share|cite|improve this answer











          $endgroup$



          The simple "secret" to ace any class is to be ahead of the class. If you can lay your hands on the course material upfront then you can stay ahead. But at the end of the day, you will learn a lot more engaging on sites like stackexchange :)







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          answered Dec 5 '12 at 1:19


























          community wiki





          broccoli






















              1












              $begingroup$

              This is an old question, but for the benefit of future readers I would like to mention Stephen Abbott's Understanding Analysis. In my opinion, this book is written at a slower pace than Rudin, and takes the reader through each step of the way. It's harder to get lost on this book, for a beginner, compared to Rudin. It goes reasonably deep for a first course as well, ending off with things like Baire's Category Theorem. So while it might not replace Rudin, it is definitely beneficial to use it as a supplement, or to get a "softer" approach first.






              share|cite|improve this answer











              $endgroup$

















                1












                $begingroup$

                This is an old question, but for the benefit of future readers I would like to mention Stephen Abbott's Understanding Analysis. In my opinion, this book is written at a slower pace than Rudin, and takes the reader through each step of the way. It's harder to get lost on this book, for a beginner, compared to Rudin. It goes reasonably deep for a first course as well, ending off with things like Baire's Category Theorem. So while it might not replace Rudin, it is definitely beneficial to use it as a supplement, or to get a "softer" approach first.






                share|cite|improve this answer











                $endgroup$















                  1












                  1








                  1





                  $begingroup$

                  This is an old question, but for the benefit of future readers I would like to mention Stephen Abbott's Understanding Analysis. In my opinion, this book is written at a slower pace than Rudin, and takes the reader through each step of the way. It's harder to get lost on this book, for a beginner, compared to Rudin. It goes reasonably deep for a first course as well, ending off with things like Baire's Category Theorem. So while it might not replace Rudin, it is definitely beneficial to use it as a supplement, or to get a "softer" approach first.






                  share|cite|improve this answer











                  $endgroup$



                  This is an old question, but for the benefit of future readers I would like to mention Stephen Abbott's Understanding Analysis. In my opinion, this book is written at a slower pace than Rudin, and takes the reader through each step of the way. It's harder to get lost on this book, for a beginner, compared to Rudin. It goes reasonably deep for a first course as well, ending off with things like Baire's Category Theorem. So while it might not replace Rudin, it is definitely beneficial to use it as a supplement, or to get a "softer" approach first.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








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